How do you factor this? 2z^2-12z+10=0
2 answers:
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Answer:
4.11 miles.
Step-by-step explanation:
In the image that I am going to attach we can see the description of the statement in a graph, now, the right triangle is formed, and we can apply Pythagoras, and the hypotenuse would be equal to:
(5 ^ 2 + x ^ 2) ^ (1/2)
The speed is equal to:
V = d / t, therefore the time is t = d / V, the total time would then be:
total time = (5 ^ 2 + x ^ 2) ^ (1/2) / 3 + (7-x) / 6
we derive with respect to x, and we are left with:
dt / dx = x / (3 * (5 ^ 2 + x ^ 2) ^ (1/2)) - 1/6 = 0
x / (3 * (5 ^ 2 + x ^ 2) ^ (1/2)) = 1/6
6x / (3 = (5 ^ 2 + x ^ 2) ^ (1/2)
(2 * x) ^ 2 = (5 ^ 2 + x ^ 2)
4 * x ^ 2 = 25 + x ^ 2
3 * x ^ 2 = 25
x ^ 2 = 25/3
x = 2.88
now we replace
7 - x = 7 - 2.89 = 4.11
In other words, the answer is 4.11 miles.
Answer:
The formula is
The 14th term is 40, in other words,
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Explanation:
The given sequence is 1, 4, 7, 10, ...
Subtract each adjacent term:
- 4-1 = 3
- 7-4 = 3
- 10-7 = 3
This shows that each term is increasing by 3. This is the common difference, so d = 3.
The first term is
The nth term of the arithmetic sequence is...
As a check, let's plug in say n = 3 to find that:
The third term is 7, which matches with the sequence given to us. I'll let you confirm the other values.
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We'll repeat this idea but now for n = 14 to find the 14th term of the sequence.
The 14th term is 40.
You can make a table of values to help confirm the answer. In the first column you'll have the values of n (1,2,3,...) all the way up to 14. The second column will consist of the sequence 1, 4, 7, 10, ... each time going up by 3 until you reach the 14th term of 40.